Kevin Avery is a bit of an overachiever when it comes to saving for retirement. He's only 25 and has nearly $40,000 in savings in his 401(k) and Individual Retirement Account.

That's quite a good start, considering the average Generation X and millennial worker has only $8,792 in retirement savings, according to a 2005 U.S. Bureau of Labor Statistics report.

But Avery says he is a bit discouraged now that President Barack Obama wants to put a cap on retirement savings. In his April budget, Obama proposed limiting the total amount workers could save from all types of retirement accounts—including 401(k)s, defined benefit plans and IRAs—to an amount that would equal, in today's dollars, a $205,000 annuity payable at age 62.

The amount, which roughly equals $3.4 million in today's numbers sounds sky-high, but under current interest rates, the amount could affect many average workers. In fact, Alicia Munnell, director of the Center for Retirement Research at Boston College, says workers who invest $7,500 annually from age 20 to 70 could possibly hit $3 million, assuming a 7 percent rate of return.

Avery seems well on his way.

"I feel like 401(k)s were built to help me live the American dream, and this puts a cap on it," says Avery, a business service representative for Red River Credit Union in Texarkana, Texas. "I don't feel we should be penalized for saving for the future. That's what we are told to do."

Obama's proposal attempts to reel in dollars for the government—$9 billion over 10 years. The U.S. Treasury Department's so-called "Greenbook," which gives detailed explanations for the 2014 budget proposal, says that while there are laws capping annuities from defined benefit plans, as well as limits for annual contributions to defined contribution plans, there are no current rules limiting workers from accumulating large amounts of retirement money from multiple accounts.

"Such accumulations can be considerably in excess of amounts needed to fund reasonable levels of consumption in retirement and are well beyond the level of accumulation that justifies tax-advantaged treatment of retirement savings accounts," the Greenbook says.

Obama Press Secretary Jay Carney said at a press briefing that it's a "no-brainer" to cap retirement benefits on wealthy people who are able to save $3 million for retirement, when most Americans are only putting away a few thousand dollars each year.

"So what the budget does is it says that once you have an amount sufficient to finance an annuity of $205,000 a year … you should not get the tax-exempt treatment on" retirement accounts, Carney said at the April 10 briefing.

But the Employee Benefit Research Institute's analysis shows the administration's ceiling will affect more than wealthy Americans. Because the administration wants to pool all retirement plans for each saver, the Washington-based think tank says the proposal would affect 20 percent of Americans ages 25 to 64 with retirement plans.

"You are going to have a lot of people hit by the limit, and then you have to think about what this is going to do to encourage employers to start or continue 401(k)s," says Jack VanDerhei, EBRI's research director.

"Every year, every taxpayer with a 401(k) and/or a defined benefit plan will need to gather all their information [from potentially different sources] to figure out whether they are over the cap," he says. "There is no way this creates the same incentives to continue 401(k)s."

Judy Miller, director of retirement policy at the American Society of Pension Professionals & Actuaries, agrees with VanDerhei, saying the proposal—and the uncertainty of it—will discourage small-business owners from starting 401(k) plans. Her Washington-based association is currently working on revenue-generating proposals that would favor plan formation.

"Small-business owners need to feel like they are getting something out" of sponsoring a retirement plan, Miller says. "This is a voluntary system, and we want to encourage the administration to look at things that will increase revenue, but not discourage employers from sponsoring retirement plans."